A new approach to the \(H_{\infty}\) design of optimal digital linear filters. (English) Zbl 0678.93063

Elsayed, A.; Grimble, M. J.

IMA J. Math. Control Inf. 6, No. 2, 233-251 (1989).

Summary: A novel approach to the solution of the \(H_{\infty}\) estimation problem is developed. The solution is arrived at by embedding the problem within a fictitious mathematically equivalent \(\ell_ 2\) framework in which a stable prefilter is introduced at the input of each noise source. The development is straightforward and relies on a polynomial system technique. Two numerical examples are presented to demonstrate the proposed approach.

MSC:

93E11	Filtering in stochastic control theory
93E10	Estimation and detection in stochastic control theory
46J15	Banach algebras of differentiable or analytic functions, \(H^p\)-spaces